square (prime+square)
Dean Hickerson
dean at math.ucdavis.edu
Fri Mar 28 23:05:15 CET 2003
Ralf Stephan (ralf at ark.in-berlin.de) asked:
> the oeis, with my help, came up with the following conjecture.
> Is it trivial?
...
> %N A075555 Smallest prime p such that p+n is a square, 0 if no such p seems
> to exist, 1 if it has been proven.
...
> %C A075555 Conjecture: a(n)=0 iff n=A047845(i)^2, i.e. there are no squares
> of the form p+k^2, p prime, 2k+1 composite.
The "i.e." seems to be unjustified. As others have noted, it's trivial that
if n is the square of an element of A047845 then a(n)=0. But it's not clear
that those are the only values of n for which a(n)=0. It would follow from
Schinzel's hypothesis, but I don't believe this special case has been proved.
Dean Hickerson
dean at math.ucdavis.edu
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